✦ LIBER ✦
Remarks on A-branes, mirror symmetry, and the Fukaya category
✍ Scribed by Anton Kapustin; Dmitri Orlov
- Publisher
- Elsevier Science
- Year
- 2003
- Tongue
- English
- Weight
- 128 KB
- Volume
- 48
- Category
- Article
- ISSN
- 0393-0440
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✦ Synopsis
We discuss D-branes of the topological A-model (A-branes), which are believed to be closely related to the Fukaya category. We give string theory arguments which show that A-branes are not necessarily Lagrangian submanifolds in the Calabi-Yau: more general coisotropic branes are also allowed, if the line bundle on the brane is not flat. We show that a coisotropic A-brane has a natural structure of a foliated manifold with a transverse holomorphic structure. We argue that the Fukaya category must be enlarged with such objects for the Homological Mirror Symmetry Conjecture to be true.